I am using docplex to solve an MILP problem. It is a minimization problem and takes a quite long time to solve. So I set the time limit to be an hour and get the best bound and MIP gap. I first solved the linear relaxation(LP) for the original problem and the original problem plus my user cuts, let's call them MILP-model and Usercut-model. They all reach their optimal and the results show my user cuts do improve the objective function value. But when I solved them as MIP, the terminating best bound for the Usercut-model gets smaller than the MILP-model, also the MIP gap gets larger. This makes me confused. User cuts are supposed to increase the bound for this problem. But why does it get smaller? Can anyone help me? Here are log files for both their LPs and MIPs. Thanks.

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Bin Tian
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#DecisionOptimization

CPLEX finds what appears to be the optimal solution fairly quickly in both models. If you compare the first two columns (Node and Nodes Left), you will see that CPLEX needs more time per node when you add the cuts than when you do not. That's not entirely surprising, since you added over 12,000 cuts. Your hope in adding cuts is that they will tighten the lower bound enough to let CPLEX prune nodes earlier and process fewer total nodes. That could still happen if you let both version run to completion. As of the one hour mark, however, CPLEX has processed around 59,000 nodes in the run with cuts versus around 81,000+ nodes without the cuts, which helps explain the superior lower bound.

At the one hour mark, the run with cuts has about 78% of visited nodes still alive versus about 81% still alive in the run without cuts. So the cuts are having some effect, but arguably not enough to justify their use.

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Paul Rubin
Professor Emeritus
Michigan State University
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